Questions about models for the valuation of option contracts.

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How does one go from measure P to Q(risk-neutral) when modeling an asset paying dividends?

I am really having a terrible time applying Girsanov's theorem to go from the real-world measure $P$ to the risk-neutral measure $Q$. I want to determine the payoff of a derivative based an asset ...
4
votes
1answer
272 views

Reference on Electronic volatility trading [duplicate]

Possible Duplicate: Looking for a recommendation for a real life volatily trading book. I recently came in contact with a quant desk that traded volatility. The discussion only highlited my ...
5
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4answers
2k views

How to get greeks using Monte-Carlo for arbitrary option?

Let's assume I have an arbitrary option that I can price using Monte-Carlo simulation. What is the general approach (i.e. without relying on specific option type) to calculating the greeks in this ...
3
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2answers
140 views

What mathematical characteristics are required from the asset price process in order to stay within the RNP framework?

I'm currently doing a course in derivatives pricing and I'm having some trouble wrapping my head around the sweet spot where theory meets reality in terms of Risk Neutral Pricing. I know that the ...
3
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4answers
1k views

Ways of treating time in the BS formula

The Black-scholes formula typically has time as $\sqrt{T-t}$ or some such. My questions: What is the granularity of this? If we treat $t$ as the number of days, then logically on the day of expiry, ...
5
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2answers
368 views

A few questions about signs of the Greek letters

Rho is the partial derivative of the value of call option, $C$, w.r.t the riskfree interest rate $r$: $$\rho \equiv \frac{\partial C}{\partial r}$$ In the standard B-S formula this term is positive, ...
3
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1answer
157 views

Parameter estimation using martingale measures - include real world data?

Please note: I posted this in nuclearphynance first, but didn't get any replies. For desks which sell exotics it is common practice (as far as I know it) to calibrate the model (Stochastic ...
5
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2answers
249 views

How to think about pricing this weather call option

So as opposed to the normal structure using a reference temperature and HDD/CDD, I'm looking at pricing a call option with a structure similar to the following: Daily option on maximum daily ...
4
votes
3answers
391 views

Is it possible to demonstrate that one pricing model is better than another?

Take the classic GBM (geometric Brownian motion) model for equities as an example: ds = mu * S * dt + sigma * S * dW. It is the basis for the classic ...
4
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0answers
421 views

ATM volatility versus OTM volatility and directional standard deviation

The forward instrument vol curve is skewed to the downside (50 delta risk reversal, 25 put, 25 call) were trading several ticks to the put). Is there a smaller standard deviation (in price terms) to ...
6
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2answers
3k views

What causes the call and put volatility surface to differ?

I currently have a local volatility model that uses the standard Black Scholes assumptions. When calculating the volatility surface, what causes the difference between the call volatility surface, ...
6
votes
1answer
138 views

Should we apply practical constraints on the distribution of monte carlo paths?

to limit interest rate paths to a 'reasonable' range (if we could define reasonable). Now we calibrate log-normal skew and mean reversion monthly to robust basket of atm swaptions and in and out ...
8
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1answer
771 views

How to 'calibrate' simple pricing models for equity index options and equity options?

I am interested in doing some research on plain vanilla equity options and equity index options. I have historical data for these options. I also happen to have market maker 'fair price' (bid and ask) ...
6
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4answers
2k views

How does an option's time value depend on moneyness?

How does an option's time value (also known as extrinsic or instrumental value) depend on how far it is in the money or out of the money? In other words, how does the time value change as the ...
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4answers
2k views

True or False? An option's price will always be greater than or equal to its intrinsic value

Since if the option's price is lower than its intrinsic value (eg. strike price - current stock price for puts), then an arbitrage opportunity arises from buying the option at bargain and then ...
3
votes
1answer
280 views

Which approach is better for modeling option exercise strategies, rational or behavioral?

This question is most relevant to the evaluation of embedded options, such as the refinancing option granted to borrowers in the mortgage and bank loan markets, or the call option present in some ...
5
votes
1answer
534 views

How to apply quasi-Monte Carlo to path-dependent options?

Following up on my recent question on variance reduction in a Cox-Ingersoll-Ross Monte Carlo simulation, I would like to learn more about using a quasi-random sequence, such as Sobol or Niederreiter, ...
7
votes
1answer
329 views

How to reduce variance in a Cox-Ingersoll-Ross Monte Carlo simulation?

I am working out a numerical integral for option pricing in which I'm simulating an interest rate process using a Cox-Ingersoll-Ross process. Each step in my Monte Carlo generated path is a ...
3
votes
1answer
164 views

Analysis of Unbalanced Covered Calls

Hello I am doing an analysis on covered calls with and extra amount of naked calls. Ignore the symbol and current macroeconomic events. I couldn't find any reference to this strategy (unbalanced is ...
0
votes
1answer
280 views

Does an option's price “ratio” with the underlying security price?

I'm trying to understand option pricing better. Let's say security ABC is \$40, and a 38 PUT option with 40% implied volatility (and 90 days till expiration) is priced at X. If security ABC then ...
7
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2answers
2k views

Are there comprehensive analyses of theta decay in weekly options?

Are there comprehensive analyses of how much theta a weekly options loses in a day, per day? I know what the shape of theta decay looks like, in theory, where the decay towards zero happens more ...
4
votes
1answer
250 views

What are good conditions to roll a leap further out in time?

If you're hedging with a back month / leap option, what are good underlying / market conditions to move this option out even further in time? For simplicity, let's say you own a call with 6 months ...
4
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4answers
1k views

How to price a calendar spread option?

How do you price calendar spread options, that is, options on the same underlying and the same strike but different times to maturity? Clarification: I'm interested in the pricing of a a CSO ...
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1answer
351 views

Calculating Theta assuming other variables remain the same

Is there any way to calculate theta at X day in future based solely on knowing 1) Total Current Option Price 2) Days Till Expiration How would this be done? Thank you
4
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1answer
341 views

Standard Deviations out the money where options will respond to underlying asset price changes

Is there an understood way of determining how far out the money an option can be, before it starts/stops responding to the underlying asset price changes? I usually look at the greeks, gamma, delta, ...
2
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0answers
189 views

Tian third moment-matching tree with smoothing - implementation

I was wondering if someone has an implementation of the Tian third moment-matching tree (http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1030143) with smoothing in code (e.g. c++, vba, c#, etc.)? ...
8
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1answer
402 views

Option Portfolio Risk - Volatility/Skew - practical implementation

I'm trying to improve my methods for calculating real-time US Equity option portfolio risk. My main problem is volatility "stability" across all strikes in an option series. The current ...
5
votes
1answer
318 views

How to value a floor when a loan is callable?

Certain bank loans pay a spread above a floating-rate interest rate (typically LIBOR) subject to a floor. I would like to find the value of this floor to the investor. Assume for this example that ...
4
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0answers
157 views

Use of Local Times in Option Pricing

I know two applications of local time in option pricing theory. First, it allows a derivation of Dupire's formula on local volatility in a neat way (i.e. without resorting to differential operator ...
8
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3answers
556 views

Reference on Markov chain Monte Carlo method for option pricing?

I have to implement option pricing in c++ using Markov chain Monte Carlo. Is there some paper which describes this in detail so that I can learn from there and implement?
8
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2answers
1k views

Why doesn't Black-Scholes work in discrete time?

I have a question considering Financial markets in discrete Time: One of the main theorems in discrete time is: In finite discrete Time with trading times t={1,...,T} the following are equivallent: ...
8
votes
3answers
2k views

How does volatility affect the price of binary options?

In theory, how should volatility affect the price of a binary option? A typical out the money option has more extrinsic value and therefore volatility plays a much more noticeable factor. Now let's ...
9
votes
3answers
1k views

What tools are used to numerically solve differential equations in Quantitative Finance?

There are a lot of Quantitative Finance models (e.g. Black-Scholes) which are formulated in terms of partial differential equations. What is a standard approach in Quantitative Finance to solve these ...
5
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1answer
957 views

Can anyone give me a practical example of pricing and calculating IV on equity index options? (i.e. using real market data)

I have been trading (mostly equity and equity index) options for a while now and I want to apply a slightly more quantitative approach to my trading - specifically, by calculating IV and incorporating ...
12
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3answers
648 views

How to price a volatility-index option?

There exist several volatility indices, such as the CBOE Volatility Index (VIX). There are also options on such indicies. What is the best way to price a volatility-index option? Is there a simple ...
8
votes
1answer
232 views

How should FX options be priced when a currency is artificially capped?

The question is inspired by yesterday's (06/09/11) historic announcement by the Swiss National Bank that it would impose a ceiling on the franc of 1.20 against the euro. I would like to know if there ...
8
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3answers
2k views

How can one compute the Greeks on VIX Futures

I am guessing the short answer to this question is "use the chain rule and linearity of the derivative," but I am looking for more specific advice on how to compute the derivatives of a VIX futures ...
13
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2answers
697 views

Duality between constant rebalanced portfolio (CRP) and corresponding derivative

One of the greatest achievements of modern option pricing theory is finding corresponding dynamical trading strategies in linear instruments with which you can replicate and by that price derivative ...
9
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3answers
1k views

How to solve for the implied stock lending rate given equity options prices?

When market makers price options on hard-to-borrow equities, they include the cost to borrow the underlying equity that their broker is going to charge them to sell the security short to hedge. I'm ...
2
votes
3answers
2k views

Why are exotic options most popular in FX?

I was reading Derman's latest blog post on Vanna Volga pricing, which, according to the linked Wikipedia article, is used mostly for pricing exotic options on foreign exchange (FX). This Willmott ...
8
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3answers
5k views

How should I calculate the implied volatility of an American option in a real-time production environment?

There are many models available for calculating the implied volatility of an American option. The most popular method, employed by OptionMetrics and others, is probably the Cox-Ross-Rubinstein model. ...
0
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1answer
221 views

What are the rules for quoting option prices on the market?

I have implemented a monte carlo pricer for an option. I simply don't know how many decimals I need to include in the quoted price. Can anyone please provide guidelines?
4
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2answers
442 views

Debunking risk premium via “hedging” argument? (or why even in the real world $\mu$ should equal $r$)

Since I began thinking about portfolio optimization and option pricing, I've struggled to get an intuition for the risk premium, i.e. that investors are only willing to buy risky instruments when they ...
2
votes
2answers
3k views

How do I estimate convergence in monte carlo methods?

I am experimenting with Monte Carlo methods. I'd like to measure/estimate convergence with a graph/chart. How do I do that? Can anyone please direct me to relevant documentation/links or even give me ...
5
votes
1answer
179 views

How to scale option pricing components in regard to time

I am looking at closed-form options approximations, in particular the Bjerksund-Stensland model. I have run into a very basic question. How should I scale the input variables in regard to time? My ...
8
votes
1answer
454 views

What are important model and assumption-free no-arbitrage conditions in options trading?

In the paper "Why We Have Never Used the Black-Scholes-Merton Option Pricing Formula" (Espen Gaarder Haug, Nassim Nicholas Taleb) a couple of model-free arbitrage conditions are mentioned which limits ...
6
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0answers
245 views

Transformation of Volatility - BS

I have recently seen a paper about the Boeing approach that replaces the "normal" Stdev in the BS formula with the Stdev \begin{equation} \sigma'=\sqrt{\frac{ln(1+\frac{\sigma}{\mu})^{2}}{t}} ...
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5answers
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What are some useful approximations to the Black-Scholes formula?

Let the Black-Scholes formula be defined as the function $f(S, X, T, r, v)$. I'm curious about functions that are computationally simpler than the Black-Scholes that yields results that approximate ...
4
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1answer
549 views

Better understanding of the Datar Mathews Method - Real Option Pricing

in their paper "European Real Options: An intuitive algorithm for the Black and Scholes Formula" Datar and Mathews provide a proof in the appendix on page 50, which is not really clear to me. It's ...
3
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1answer
293 views

European turbo warrants

Totally new to the world of quant finance, so perhaps this is an odd question... Does there exist an American equivalent to the German style "knock out zertifkate"? (The name might be slightly ...